REGULAR PAPER

Japanese Journal of Applied Physics 55, 022701 (2016)
http://doi.org/10.7567/JJAP.55.022701

Real-time displacement measurement system using phase-shifted optical pulseinterferometry: Application to a seismic observation system
Minoru Yoshida1*, Yoshiharu Hirayama1*, Atsushi Takahara1, Motofumi Kashi1, Keiji Takeuchi1, Toshiharu Ikeda1,
Fumio Hirai1, Yosuke Mizuno2, Kentaro Nakamura2, Hitoshi Kimura3, Norio Ino3, and Wataru Inoue3
1

Hakusan Corporation, Fuchu, Tokyo 183-0044, Japan
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan3
Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan2*E-mail: yoshida@hakusan.co.jp; hirayama@hakusan.co.jp
Received May 21, 2015; accepted November 18, 2015; published online January 18, 2016
We developed a method of detecting incident light levels on the oscillator surfaces and light pulses that include two interfering pulses with a phaseshift of π/2 (phase-shifted optical pulse interferometry). This system enables the measurement of displacements greatly exceeding the half
wavelength of the laser. Moreover, it allows measurements at multiple locations with a single optical ﬁber for using optical pulses. In this study, we
conducted an interference experiment using 30 ns optical pulses and transmitted them at 1 µs intervals. We conﬁrmed that the above two
measurements are possible. Furthermore, from the data of the oscillator used for veriﬁcation, we showed that measurements on the order ofnanometers are possible. Since this method does not require a power supply to the oscillator, its widespread applications in physical exploration
can be expected. © 2016 The Japan Society of Applied Physics

1.

Introduction

In earthquake observation, ground motion is measured using
an accelerometer and a velocity meter (called a seismometer);the measured data are used to determine the earthquake
mechanism, ground structure, and internal structure ofEarth.1–3) Furthermore, when observing volcanoes, a seismometer is used to estimate the position and scale of amagma chamber to verify the mechanism of eruptions andpredict volcanic eruptions.4–6) To examine the mechanismof an earthquake hypocenter in detail, seismometers must
be positioned around the epicenter. However, earthquakes
associated with subducting plates often have epicenters in
the ocean. Therefore, seismic observation only on land isinsuﬃcient, and earthquake observation networks have been
installed on the sea ﬂoor around Japan as well as in otherparts of the world.7–9) In the ﬁeld of geophysical exploration,
which includes resource exploration, observations are madeat multiple points in a wide area to improve the resolution.
Therefore, in sea-ﬂoor exploration, sensors that do not
require a power supply and a system that uses optical ﬁber fortransmission are desired.10,11)
There are several methods for measuring acceleration
using optical ﬁbers. For example, there are methods using the
Fabry–Perot interferometer,12,13) amplitude modulators,14)
and diﬀerential optical detectors;15) others measure the vibration of a micromachine silicon cantilever with light-density
modulation using multimode ﬁbers,16) involve ﬁber Bragg
gratings (FBGs),10,11,17–23) or are interferometric methods.24–27) Among these, FBG10,11,21) and interferometric25)
methods are primarily used for actualizing frequencies of
0.1 to several hundreds of Hz, which are necessary inearthquake observations including geophysical exploration,with a dynamic range of 100 dB.
FBG methods mainly use the measurement principle ofa contact-type hydrophone, and optical ﬁbers are wrappedaround seismometers such as moving-coil-type seismometers. There exists a method to convert the vibration of thespindle inside a seismometer to the expansion and contractionof optical ﬁbers to detect vibration;10,11) another method uses

the optical ﬁber itself as an accelerometer.21) These methods
do not require a power source between the ﬁbers and thesensor; thus, they are currently used in sea-ﬂoor earthquake
observation.
In the FBG methods,28) it is generally necessary to use an
FBG with a central reﬂection wavelength that is diﬀerent in
the number of multi points, although there are exceptions.
Therefore, a wide-bandwidth light source that covers theentire wavelength range or a frequency-sweep light source isrequired, which is a disadvantage.
In contrast, interferometry enables measurement using asingle-wavelength laser and is advantageous in that its
sensitivity can be increased. For example, Zumberge et al.25)
measured the vibration of an STS1 seismometer in real timeand conducted phase unwrapping. Assuming that an amplitude of several centimeters is captured with a resolution lessthan 1 pm, they showed that the performance of the STS1
seismometer can be maximized by light interferometry.
The impact of these results was signiﬁcant in the ﬁeld ofearthquake observation, especially as it presented a goodprospect for high-precision observation that does not requirea power source for the sensor. However, their proposed
method uses continuous light; thus, creating multi points inthe measurement system using a time-division multiplex isdiﬃcult.
In this paper, we propose phase-shifted optical pulseinterferometry, which enables the easy integration of multiple
observation points for application to a seismometer. Shindo
et al.29) provided a description of the method of using opticalpulses and multiple observation points. In their interference
method, they attached the ﬁber directly to the oscillator
and observed the expansion and contraction of the oscillator
during vibration using interference. Therefore, although a
power supply is not required for the sensor, there is a
disadvantage in that the oscillator amplitude cannot bemeasured beyond the half wavelength of the pulsed light.
Our method applies a pulse with a partial π=2 phasemodulation to the front and back surfaces of a springsuspended mass. When optical pulses are made to interfere by
applying an appropriate delay on one side of the spring-

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M. Yoshida et al.

suspended mass, the light incident on the spring-suspended
mass can also be measured and the changes in incident lightintensity due to environmental ﬂuctuations can be removed.
Simultaneously, phase unwrapping becomes possible, whichallows the measurement of a displacement that exceeds half
the wavelength. A prototype of the spring-suspended mass
was prepared, and a vibration measurement was conductedwith the proposed light interferometry method to show thatthe measurement of a displacement that greatly exceeds the
wavelength of the incident light is possible, as indicated by theprinciple. We also showed from the observation record of thespring-suspended mass that nanometer-order measurement ispossible. Furthermore, by using a 30 ns optical pulse transmitted at 1 MHz, we conducted a simultaneous experiment
for the two sensors to show that measurement at multiple
locations is possible. For this transmission condition, measurement with up to 20 sensors is possible in a calculation.
2.

(a)Phase-shifted optical pulse interferometry

Generally, to measure the interference signal obtained
through light interferometry, the phase diﬀerence θ between
the reference light r and the measurement light s is obtained.
The electrical signal level I of interference light i resulting
from interference between the reference light r and measurement light s is expressed aspﬃﬃﬃﬃﬃﬃ
I ¼ jr þ sj2 ¼ R þ S þ 2 RS cos :
ð1Þ
At this time, R, S, and I are the electric signal level of thereference light r, measurement light s, and interference light i,
respectively, which are equal to the square of the eﬀective
amplitude of each light. In the conventional method, R and S
are treated as constants; therefore, the variation error due tointensity ﬂuctuation on the transmission pathway could not be
separated, implying that the conventional method is unsuitable for a measurement that requires long-term stability, suchas a ﬁeld observation. In the present study, the light signal
was pulsed and made to interfere with the reference light byappropriately delaying the measurement light. This allows
for a design in which the interference output pulse can beobtained as a time-division multiple pulse of the portion of thereference light only R, interference light portion I where thereference light and measurement light overlap, and the portionof the measurement light only S. Thus, the electric signal
levels R, I, and S can be obtained simultaneously. Consequently, cos θ can be obtained using Eq. (1).
Questions that use Eq. (1) are output with cos θ ranging
from −1 to 1; however, because the measurement error is solarge that ∣cos θ∣ is closer to 1, it is necessary, in practice,pto
ﬃﬃﬃ
take measurements within the range of j cos j < 1= 2,
where good linearity exists. Therefore, a light accelerometerwith an automatic drift compensation function built into thelight source has already been created so that θ is constantly
around π=2.30) However, in this method, only a displacement
shorter than half the wavelength can be measured, limiting
the dynamic range.
The method proposed in the present study allows for continuous measurement without adjusting the phase of the lightsource. Two pulses with phases diﬀering by π=2 are used, as
shown in Fig. 1(a). The reference light interferes with themeasurement light, which is delayed by τ, to obtain two
interference outputs, namely, I1 and I2, in addition to R and S.

(b)
Fig. 1. (Color) (a) Schematic diagrams of reference light, measurement
light, and interference light. (b) Schematic diagram of phase-shifted opticalpulse interferometry.

If the input pulse length in Fig. 1(a) is 3τ, π=2 phasemodulation is applied only to the ﬁnal τ. Through interference resulting from applying a delay τ to the input pulse
on one side of the vibration plane, an output pulse with length4τ is obtained. At this time, the following holds:
ðI1  R  SÞ
pﬃﬃﬃﬃﬃﬃ ;2 RS
ðI2  R  SÞ

pﬃﬃﬃﬃﬃﬃ ; 2 ¼ 1  :cos 2 ¼
2
2 RS
By taking the ratio of (2) and (3),cos 1 ¼

cos 2sin 1ðI2  R  SÞ:¼
¼ tan 1 ¼
ðI1  R  SÞcos 1 cos 1
Therefore,
1 ¼ tan1I2  R  S
I1  R  S¼ cot1
I1  R  S:
I2  R  S

ð2Þ
ð3Þ

ð4Þ

ð5Þ

Hereafter, θ1 will be written as θ.
In the tangent function, θ diverges at ±π=2, while in the
cotangent function, θ diverges at 0 and π. To avoid thesedivergence points, we chose the function with the absolutevalue closer to 0 in order to calculate θ in the range   <  as follows:

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M. Yoshida et al.

8




 I2  R  S >
1 I2  R  S
>


>
tan
when
<
I  R  S  1
I1  R  S
1




: ð6Þ
¼
 I2  R  S >>
1 I1  R  S


>
>
1
cot
when
:
I  R  SI2  R  S
1The variation Δθ(t) at a time t is calculated from θ obtainedfor every sampling interval Δt:ðtÞ ¼ ðtÞ  ðt  tÞ:

ð7ÞWhen the above value exceeds π, 2π is subtracted; whenthe value is below −π, 2π is added for adjustment.
The variation Δθ(t) is the quadruple of the phase diﬀerence
caused by the amplitude of the actual oscillator. As shownin Figs. 1 and 5, this is due to the interference of light thatwas measured on both sides of the oscillator.
If θA is assumed as Δθ when the sampling interval Δt is
suﬃciently small, the actual phase change Θ(t) is calculatedasZtðtÞ ¼
 0 dt:ð8Þ
0

The calculated displacement D(t) can be obtained bymultiplying Θ(t) by the wavelength of the measurement
light λ asZ
 t 0DðtÞ ¼
 dt:
ð9Þ
2 0
In this method, as long as the measurement is within range,
there is no limit to the number of phase unwrapping steps.
We call this interferometry as phase-shifted optical pulseinterferometry.
3.

Spring-suspended mass as an accelerometer

3.1

Measurable range

The condition that enables phase unwrapping through phaseshifted pulse interferometry allows for the determination of
the vibration direction with Δθ ; thus,jðtÞj <; i:e:, jDðtÞj < ¼
2
2 2 4

ð10Þ

must be true.
At this point, let us assume that the spring-suspended
mass vibrates at the displacement dðtÞ ¼ A sinð2 f tÞ. The
maximum displacement rate of this spring-suspended massd(t)max is 2π fA. Therefore, the maximum change in displacement, ∣Δd(t)∣, with the sampling rate of the laser light F (Hz)is 2π A f=F. As we will discuss in Sect. 4.1, if the design
allows for interference with a reﬂected wave on applying an
optical pulse from both sides of the spring-suspended mass,
the light path of the optical pulse D(t) becomes four times
the actual displacement of the spring-suspended mass d(t).
Therefore, the condition for the maximum amplitude of themeasurable spring-suspended mass A and frequency f isjDðtÞj ¼ j4dðtÞj ¼

8Af 
< :
F
4

ð11Þ

Since this system is a magnifying structure, it is possible
to enlarge ﬁne ﬂuctuations and capture them. Hence, it has
the advantage of precision.
If the wavelength and sampling rate of the laser light used
are 1.55 µm and 1 MHz, respectively, the amplitude A mustFig. 2. Amplitude characteristics of an accelerometer.

be less than 1.55=(32π f ) m. For example, it is possible toobserve a vibration with f = 10 Hz as long as the amplitude Aof the spring-suspended mass is less than 1.5 mm.
3.2 Preparation of the spring-suspended mass as anaccelerometer

To apply the phase-shifted optical pulse interferometry to theobservation of vibrations such as earthquakes, we prepared aspring-suspended mass as an accelerometer. When measuring
vibrations such as ground motions using a spring-suspended
mass, a damping force proportional to the velocity of thespring-suspended mass is typically applied. The equation of
motion for such a system is31)
d2y
dy
d2x
þ 2 þ !20 y ¼ 2 ;
2
dt
dt
dt

ð12Þ

where y is the relative displacement of the spring-suspended
mass, γ (= hω0) is the attenuation rate, h is the attenuation
constant, ω0 is the natural angular frequency of the springsuspended mass, and x is the displacement input fromoutside.
The frequency characteristics of a seismometer are
generally expressed as a response when a sine-wave groundmotion is applied. Considering x(t) = sin ωt with ω = 2π=T,
we obtainyðtÞ ¼ Uð!Þ sin½!t þ ð!Þ;

ð13Þ

where
!2
2!
Uð!Þ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ and tan  ¼ 2:!0  !2ð!20  !2 Þ2 þ 42 !2Regarding the amplitude in Eq. (13), the normalized
displacement amplitude of the spring-suspended mass isexpressed in a graph with a normalized frequency (Fig. 2). Ifω ≪ ω0, the amplitude of y(t) does not depend on the input
frequency, but instead takes a value depending on the input
acceleration.
In actual seismometers, the damping factor is of the orderof 0.7 to prevent an increase in vibration near the natural
frequency of the oscillator. In the case of detecting grounddisplacement, the region of ω ≫ ω0 is used, and in the case of
detecting ground acceleration, the region of ω ≪ ω0 is used.
Considering ours as a device for system veriﬁcation, we used
the region of the accelerometer where the oscillator is not
damped and conducted the veriﬁcation.

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Fig. 3. (Color) Inside of the spring-suspended mass (with the outer ﬂange
removed).

Fig. 4. (Color) 3D CAD model of the vibrating part in the sensor.

Fig. 5. (Color) Structure of the test bed in phase-shifted optical pulse interferometry. This method uses laser-pulse inputs R and S. The pulse duration is
30 ns. The phase of the last 10 ns is progressed (regressed) to π=2 against the ﬁrst 20 ns. This pulse is transmitted every 1 µs.

In a typical earthquake observation, measurements aretaken at 100 Hz or lower; therefore, a spring-suspended
mass is prepared with a natural frequency of approximately
300 Hz, along with that with a natural frequency of approximately 50 Hz to verify the measurements of large amplitudes
at the low frequency by phase-shifted optical pulse interferometry.
Sensor parts of the spring-suspended mass with a natural
frequency of approximately 300 Hz are shown in Fig. 3. The
outer shape of the sensor prepared for this study consistsof nickel-plated brass, and the total size of the sensor is
36 × 36 mm2. The spring of the sensor is made of beryllium
copper, and is the outer diameter is 25ϕ.
A three-dimensional (3D) computer aided design (CAD)
model of the vibrating part in this sensor is shown in Fig. 4.
The spring characteristics in the design of this model were as
follows: through mode analysis with the peripheral portion of
the spring ﬁxed, the primary mode was vertical against theplane of the spring, and the natural frequency was 371 Hz.
4.
4.1

Spring-suspended mass measurement system

System structure
By using the principle of phase-shifted optical pulse interferometry presented in Sect. 2, we prepared a test bed

that measures the vibration of the spring-suspended mass
discussed in Sect. 3. This system consists of a phase-shifted
optical pulse generator, a sensor signal processor, and asensor connected to the tip of an optical ﬁber (Fig. 5).
In the phase-shifted optical pulse generator, a continuous
light of 1.55 µm wavelength was generated as the interference
light source by using a highly stable laser transmitter with anarrow line width of 5 kHz. A high-speed lithium niobate(LN) intensity modulator and an LN phase modulator thatcan provide GHz-band behavior were used for the laser light,
and an optical pulse with a total pulse width of 30 ns and a
relative phase diﬀerence of π=2 at 20 ns to the front and 10 ns
to the back was generated and transmitted at 1 µs intervals.
A polarization-maintaining ﬁber was used for transmission
to the sensor. At the sensor, the optical pulse is branchedby couplers after passing through a polarizer. After reﬂecting
on reﬂexive mirrors attached to both sides of the springsuspended mass, the light interferes and enters the sensor
signal processor.
The sensor signal processor converts the light signal into
an electric signal, and subsequently conducts A=D conversion at a sampling rate of 3.6 GHz, extracting the interference pulse at intervals of 1 µs to obtain R, S, I1, and I2.
Next, it calculates the displacement from Δθ of the spring-

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(a)suspended mass that has gone through 2000th-order movingaverage processing, and it outputs with 1 MHz sampling.
A frequency band of 200 Hz or less is used in the ﬁeldof natural earthquakes and physical exploration. Therefore, as
the preliminary processing of the obtained data, we applied acomb ﬁlter that cuts oﬀ frequencies above 500 Hz. Since thisstudy involves 1 MHz sampling data, we decided to take a
2000th-order moving average.
4.2

Vibration experiment
An anti vibration table was installed for the vibration experiment. A metal box containing gel was placed on this table,
and the vibration table was placed on top of this box. As
we aimed to obtain the value of acceleration actually applied
to the spring-suspended mass, the servo-type accelerometer
JA40GA manufactured by Japan Aviation Electronics
Industry, Ltd. was also set on this table to adjust the inputof the vibration table. JA40GA is an accelerometer often used
for earthquake observations in Japan32) and is ﬂat from 0
to approximately 200 Hz, allowing measurements up to±39.6 m=s2.33)
The spring-suspended mass from Sect. 3 was placed on thevibration table. Figure 6(a) shows a Lissajous ﬁgure obtainedwith the 1 MHz sampling of a sine wave at an acceleration
rate of 2.94 m=s2, a frequency of 30 Hz, and an observation
time of 0.05 s. cos θ1 and cos θ2 were calculated using
Eqs. (2) and (3), respectively. The Lissajous ﬁgure shows achange along a true circle.
In our system, we conducted the experiment by adjusting
the phase shift of the pulse to be π=2 in the phase-shift cycleof the pulse, causing a circular display of the Lissajous ﬁgure,as shown in Fig. 6(a), and by simultaneously conﬁrming it.
When we used the ellipse ﬁtting method34) for the Lissajous
ﬁgure in Fig. 6(a), the major axis of the ellipse was 0.999, theminor axis was 0.965, and the major axis=minor axis ratio
was 1.03. In addition, the tilt of the ellipse was 0.1 rad, andwe could conﬁrm that the Lissajous ﬁgure is almost a circle.
Therefore, it is conﬁrmed that the π=2 phase shift of theincident pulse was achieved; i.e., the phase diﬀerence between
θ1 of Eq. (2) and θ2 of Eq. (3) is π=2. Furthermore, we cansee that the transfer at 2π, which exceeds the wavelength ofthe laser light in Eq. (8), is appropriately achieved. Δθ in
Fig. 6(b) was obtained by applying a 2000th-order moving
average to the results of Eq. (7), and the amplitude roughlychanged with a sine wave of 0.003 rad, conﬁrming that themeasurements were within the limit stipulated by Eq. (10).
In Fig. 6(c), the displacement of the spring-suspended
mass is approximately 1 µm, and the frequency is 30 Hz. As
shown in Figs. 6(a) and 6(b), the measurements are appropriate; thus, the displacement in Fig. 6(c) expresses the actual
displacement of the spring-suspended mass. This is a result of
the oscillator used in this study, and when the parameters of
the oscillator used such as resonant frequency and Q-valuechange, the maximum acceleration also varies.
4.3 Consistency of light interferometer record by inputting
a square wave

Next, a square wave of 0.1 Hz frequency was input into thevibration table, and a single-degree-of-freedom attenuating
vibration was measured. The displacement of the vibrationtable that uses a laser displacement meter and the acceleration

(b)

(c)

Fig. 6. (a) Lissajous ﬁgure for cos θ1 and cos θ2. (b) Values of Δθ.
(c) Waveforms obtained by integrating (b).

of the vibration table with a servo accelerometer were
simultaneously measured using one data logger with 1 kHz
sampling. We examined the consistency with the displacement of the spring-suspended mass with light interferometry
obtained at 1 MHz sampling and detected small, free natural
vibrations.
Figure 7(a) shows the acceleration of the vibration tablemeasured using the servo accelerometer and the displacementof the sensor measured using light interferometry when asquare wave of 0.1 Hz frequency and 0.55 mm amplitude was
input. Figure 7(b) shows the overlapping Fourier spectrum
for each measurement.
The damping ratio ζ calculated from the envelope ofthe sensor displacement shown in Fig. 7(a) was 0.05027.
As the attenuation is small, the displacement of the springsuspended mass will show a natural vibration of the sensor on
the line proportional to the input acceleration. The graphshowing an overlap with the acceleration measured using theaccelerometer at the same time indicates that the measured
displacement of the spring-suspended mass agrees with thetheory, implying that our technique provides correct measurements [Fig. 7(a)]. The graph showing the Fourier spectrum for each measurement [Fig. 7(b)] further conﬁrms thevalidity of the interferometry technique. When Fourier

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M. Yoshida et al.

(a)

(a)

(b)
(b)

(c)

Fig. 7. (Color) (a) Acceleration measured using the accelerometer anddisplacement of the sensor obtained using light interferometry. (b) Fourier
spectra of the accelerometer and spring-suspended mass.

analysis was conducted on the displacement of the springsuspended mass, the natural frequency was 320 Hz. This isapproximately 15% oﬀ the design value of 371 Hz indicatedin Sect. 3.2. The reason for this diﬀerence is that the springsuspended mass is not completely ﬁxed, and the spring
constant is lower than the calculated value.
Next, to conﬁrm that the spring-suspended mass captures
displacements with small free vibrations, we show the measurement values from approximately 0.3 s after adding asquare-wave displacement (Fig. 8). Figure 8(a) shows the
Lissajous expressions of cos θ1 and cos θ2 calculated using
Eqs. (2) and (3), which indicate that the phase barelychanged. Figure 8(b) shows Δθ obtained by applying a
2000th-order moving average taken for a duration of 0.01 s
from approximately 0.3 s after adding a square-wave displacement. The obtained Δθ shows sine-wave oscillation
with an amplitude of 20 µrad. The optical path diﬀerence ofthe laser light was four times Δθ, indicating that the 5 µrad
variation in the displacement diﬀerence of the springsuspended mass is captured. If the path diﬀerence is expressed as a length, that is as the wavelength of the laser lightof 1.55 µm, it is 1:55  ½5  ð106 =2Þ ¼ 1:2  106 µm;
thus, this system has the ability to capture a displacement of
1.2 pm. The displacement in Fig. 8(c) obtained using Eq. (9)is aﬀected by the integral at both ends, but the measurement
captures the displacement of a natural vibration with anamplitude of approximately 1.5 nm. In addition, when we
took the time variation obtained from the laser displacement
meter as the input quantity, carried out a dynamic simulationof the mass-spring damper system, and determined theFig. 8. (a) Lissajous ﬁgure for a duration of 0.01 s approximately 0.3 s
after inputting a square wave displacement. (b) 2000th-order moving averagefor Δθ for a duration of 0.01 s approximately 0.3 s after inputting a squarewave displacement. (c) Waveform of the displacement obtained byintegrating Δθ.

displacement with respect to the housing of the opticalsensor, we conﬁrmed that it matched well with the output
value of the optical sensor.
4.4

Connecting multiple spring-suspended masses
In addition to the structure presented in Sect. 4.1, the opticalpulse was branched using a coupler. By delaying one branch,
we can show that two spring-suspended masses can be measured with time division.
In the optical pulse generator, the optical pulse with awidth of 30 ns was prepared as indicated in Sect. 4.1 andtransmitted with 1 µs intervals. In the sensor, light passes
through a polarizer and is branched using a coupler. One
branch of the pulse is reﬂected at reﬂexive mirrors attached toboth sides of the spring-suspended mass, as in the previous
section, and then made to interfere. The other branch of thepulse is delayed by 50 ns, and then the wave reﬂected fromthe spring-suspended mass interferes in the same manner.
With this delay, the interference pulse from two springsuspended masses is transmitted to the signal processor with

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Fig. 9. (Color) Conﬁguration diagram of the test bed when conducting simultaneous multiple observations with phase-shifted optical pulse interferometry.
This method uses laser-pulse inputs R and S. The pulse duration is 30 ns. The phase of the last 10 ns is progressed (regressed) to π=2 against the ﬁrst 20 ns. Thispulse is transmitted every 1 µs.

(a)Fig. 10. (Color) Photograph of the spring-suspended mass and sensor
during observations.

a 10 ns shift; thus, the components can be sequentially output
without interference with each other (Fig. 9).
In this experiment, two spring-suspended masses with anatural frequency of approximately 50 Hz are installed on thevibration table and forced to vibrate at 35 Hz. If the parameters other than the natural frequency of the spring-suspended
masses are the same, a spring-suspended mass with a lower
natural frequency will show a higher amplitude. The amplitude of the 50 Hz spring-suspended mass is higher thanthat of the 320 Hz spring-suspended mass; therefore, while
simultaneous observations were made for the two springsuspended masses, their amplitudes were also veriﬁed. A
photograph of the observation is shown in Fig. 10. The redpart at the bottom of Fig. 10 is the vibration base thatmoves up and down. The sensor in the front is the servo-type
accelerometer, and the two parts lined on the top are thespring-suspended masses. These spring-suspended masses
can simultaneously vibrate on one vibration table.
The observation results were processed in the same manner
as before, and the displacement waveforms [Fig. 11(a)] andspectra [Fig. 11(b)] of the spring-suspended masses wereidentiﬁed. Figure 11(a) indicates that the frequencies of the(b)Fig. 11. (Color) (a) Output waveform obtained during simultaneous
vibration. (b) Fourier spectra obtained during simultaneous vibration.

two spring-suspended masses are in agreement, but thedisplacement amplitudes are diﬀerent.
Since the parts containing the spring are not exactly thesame, there is a possibility that an error may have occurred in
the thickness and length; since the oscillator conﬁguration is
not completely ﬁxed, it is likely that variations have occurred.
Since the objective of the current study is to check the022701-7© 2016 The Japan Society of Applied Physics

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Fig. 12.

M. Yoshida et al.

(Color) Schematic diagram of multiple observation points.

behavior under multiple sensors, the uniformity of sensor
performance has not been focused upon. However, since thehomogeneity of the oscillator performance is important for
future practical applications, we would like to resolve thisissue in the future.
The Fourier spectra in Fig. 11(b) indicate that, for an inputof 35 Hz, two spring-suspended masses respond in the samemanner, showing that the simultaneous measurement of
two spring-suspended masses through the interferometry
technique was successful. When simultaneously measuring
two sensors, an approximate loss of 3 dB is caused by opticalpulse branching, but it does not aﬀect the accuracy of themeasurements. If multiple points are used, the eﬀect of theloss can be removed by increasing the ampliﬁcation of thelight in the system.
The seismometer typically requires three components at
one observation station: north–south, east–west, and up–
down. Furthermore, in this system, a compensation circuit isinserted to remove the disturbances other than the springsuspended mass, implying that there is one observation pointwith four components.
If a pulse with τ = 10 ns is transmitted from the pulse
generator at 1 µs intervals, as in Fig. 12, a period of 200 ns isnecessary in the four components. By applying 200 ns foreach observation point, multiple observation points can beconnected using the same optical ﬁber. Under these conditions, at the maximum in a calculation, the interference
pulse of ﬁve observation points and 20 sensors can ﬁt within
1 µs, enabling the installation of ﬁve observation points using
one ﬁber.
5.

Discussion

As shown in Fig. 12, we constructed this system to reduce
the system noise and environmental noise by simultaneously
measuring the records of ﬁxed ends and subtracting theserecords from the record of each sensor. Incidentally, theobservation records with the ﬁxed ends showed that the noise
is low in high-frequency regions with frequencies higher than
1 Hz and in low-frequency regions with frequencies lower
than 1 Hz; the noise increased with the decrease in frequency.
Next, when the two ﬁxed ends were simultaneously measured, their noise levels were almost the same over the entire
frequency, and the noise levels obtained from the diﬀerence

between the two showed an improvement of approximately
20 dB over the entire frequency range when compared with
the noise levels separately obtained from the individual ﬁxed
ends. However, the spectral shape remains nearly unchanged
from the spectral shapes of individual ﬁxed ends, and we
found that the increasing trend of noise in the low-frequency
regions cannot be eliminated. Since the noise reduction in the
low-frequency regions is directly connected to the practicalapplicability of the broadband seismometer, an improvementin this area is a major challenge for the future.
On the other hand, if the vibration of the geophone can bedirectly measured using the proposed interferometry technique, a more detailed vibration measurement at the sensor
without a power supply can be realized in comparison withthat achieved in the previous study, in which the displacement in the spring-suspended mass vibration in the geophone
was measured as a change in capacitance by using the electric
signal.35,36)
By using the phase-shifted optical pulse interferometry
proposed in this paper, the signal levels of reference light, R,
measurement light, S, and interference light, I, can be simultaneously measured to remove the loss in the light-signal
path, enabling application in long-distance transmission.
Furthermore, by delaying the light-receiving interval of thepulse for each sensor, multiple channel measurements by thesame pulse become possible. Therefore, one can consider the
output for temperature compensation and connect multiple
sensors with ease. This characteristic will lead to a long-termand real-time monitoring network of resources without apower supply and a seismogram for deep drilling at hightemperatures. In this study, we performed measurements
using the 30 ns pulse transmitted at 1 MHz. Under these
conditions, up to 20 components can be measured using one
light source. In the future, by decreasing the optical pulse
length to one-ﬁfth, the maximum number of measureable
components can be increased to 100. Data output in thisstudy was performed at a high speed (1 MHz sampling),
and in the decimation process, measurements at 1 kHz
sampling indicated potential for resource exploration andthose at 100 Hz sampling indicated potential for earthquake
observation.
6.

Conclusions

We examined the principle of phase-shifted optical pulseinterferometry and showed that measurements using our
prototype spring-suspended mass of distances signiﬁcantly
exceeding the wavelength of the incident light are possible,
as suggested by the principle. On the basis of the record ofspring-suspended mass observation, we showed that measurements on the order of nanometers are possible. Furthermore, by using an optical pulse with a length of 30 ns transmitted at 1 MHz, we conducted a simultaneous vibration
experiment of two sensors and showed that measurement at
multiple locations with one optical path is possible. In the
future, by using a suitable spring-suspended mass, we plan todevelop an optical seismometer that is practical for ﬁeld use.
Acknowledgements

Part of this research was supported by the fund of thetechnical solution project of Japan Oil, Gas and Metals
National Corporation (JOGMEC). We express our great

022701-8© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 022701 (2016)

M. Yoshida et al.

thanks to JOGMEC for supporting this study. We express ourgreat thanks to Mr. Toru Kuroda and Mr. Yoshiaki Kawabe
of JGI, Inc., for useful discussions and advice as project
partners. We also express our great thanks to Mr. Kazumasa
Tsukada for developing the device used in this system.

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